SYLLABUS

MATH 2123

CALCULUS II FOR BUSINESS, LIFE SCIENCES, AND SOCIAL SCIENCES

 

COURSE DESCRIPTION AND PREREQUISITE

 

MATH 2123 is the second of a two-semester sequence in elementary calculus in which students use the concepts of differential and integral calculus to solve theoretical and applied problems in business, life sciences, and social sciences.

 

 

GRADING POLICY AND PROCEDURES

 

The mathematics faculty has established the following grading policy and procedures for mathematics courses numbered 1000 and above.

 

Each course will have tests and/or other assessment items such as projects or portfolios covering the course content as described in the course syllabus.  An instructor may also use quizzes, homework, attendance, bonus questions, etc. in determining a student’s course average.  Students will be informed in writing as to how their course averages will be calculated.  The following scale will determine the grade for the semester:

 

              OVERALL AVERAGE                               COURSE GRADE

 

                        90 – 100%                                                     A

                        80 -  89%                                                       B

                        70 –  79%                                                      C

                        60 -  69%                                                       D

                        Below 60%                                                    F

 

OTHER GRADE DESIGNATIONS

 

W -      (Official Withdrawal) Students may officially withdraw from a course until the end of the twelfth week of a sixteen-week semester (or ¾ of the duration of a shorter course).

 

I -         (Incomplete) An I is not an automatic option and is given ONLY at a professor’s discretion in situations of extreme extenuating circumstances.  When an extreme extenuating circumstance arises, it is the student’s responsibility to notify the professor immediately.  If an I grade is used, the professor establishes a contract with the student to specify the work which must be completed and the date for completion.  At the end of the contracted period, the professor will replace the I with the appropriate grade:  A, B, C, D, or F.

 

See the college catalog for a more complete definition of these grades.

 

 

 

 

REQUIRED COURSE MATERIALS

 

Calculus Concepts, Third Edition by LaTorre, Kenelly, Reed, Harris, Carpenter; Houghton Mifflin Company, 2005.

 

TI-83 or TI-84 graphing calculator.

 

GRAPHING CALCULATOR LEASE PROGRAM

 

The procedure for leasing a graphing calculator is as follows:

 

1.         Payment of $25.00 is made in the Bursar’s office for the Calculator Lease      Program.  The receipt will be given to the student to bring to the Math Lab.

 

2.         The student is asked to sign a lease agreement acknowledging his/her responsibility for returning the calculator in working condition along with its instruction manual upon the conclusion of the lease agreement. If the calculator is not returned, the student accepts responsibility for reimbursing the Math Lab for the full cost of the calculator.  Failure to do so will result in the student's account for this calculator being forwarded to a collection agency, a hold being placed on the student's official records, and refusal of future enrollments.

       

 

RESOURCES

 

Graphing Calculator Instruction Guide to Accompany Calculus Concepts, Third Edition by Iris  Fetta Reed.  This guide contains keystroke information adapted to material in the text for the TI-83 and the TI-86 graphing calculators.  This guide is also on reserve and available for use in both the college library and the Math Lab.  The guide can also be accessed online at the Calculus Concepts Web Site described below.

 

A Student's Solution Guide contains complete solutions to the odd-numbered activities and is available in the bookstore as an option.  It is also available for use in the Math Lab and the college library. However, it cannot be checked out and taken home from either the Math Lab or the library.

 

The Calculus Concepts Video Series contains chapter-by-chapter lectures by a master teacher.  These videos can be used by students who miss a class or by students who think they would benefit from seeing another teacher explain a particular topic.  The video series is available in the Math Lab and in the college library.

 

The Calculus Concepts Web Site (accessible through college.hmco.com) contains extra practice problems, help with algebra, practice quizzes, and other assistance.  The web icon in the text directs you the book-specific web site when appropriate.

 

Free on-line tutoring is available through SMARTHINKING.  For more information about this service, go to the Calculus Concepts Web Site at college.hmco.com.

 

A  web site (www.occc.edu/business_calculus) at Oklahoma City Community College has been set up to provide information regarding the usage of the TI-83/83 Plus calculators.  The site contains calculator solutions to examples taken out of the textbook.  

 

 

MATH LAB

 

For those who would like assistance outside the classroom, the Math Lab is strongly recommended.  The Math Lab is located in the Mathematics Center in the CLC Building.  Students are encouraged to use the Lab for:

 

1.         Studying,

2.         Asking questions of tutors or lab assistants,

3.         Checking work with solutions manuals,

4.         Problem solving using calculators and computers.

 

The hours the Math Lab is open are posted at the entrance to the Math Lab and are also available from your instructor.

 

Math Lab materials are to be used in the Math Lab only and may be obtained for use in the Math Lab from the staff with a student ID card.

 

NO Materials are to be taken out of the Math Lab.  Any violations of this policy will result in a written warning for the first offense.  A second violation will be the basis for an official complaint to the Vice President for Student Services as a violation of the Student Conduct Code.  Consult your Student Handbook for Student Disciplinary Procedures.

 

 

ACCOMMODATIONS FOR STUDENTS WITH SPECIAL NEEDS:

 

Oklahoma City Community College complies with Section 504 of the Rehabilitation Act and the Americans with Disabilities Act.  Students with disabilities who seek accommodations must make their request by: Contacting the office of Services to Students with Disabilities, located on the first floor of the Main Building near entry 12, or call 682-7520

 

ACADEMIC DISHONESTY

 

The college considers academic dishonesty a serious offense.  See the student handbook or college catalog for details.

 

MISCELLANEOUS INFORMATION

 

There is no substitute for working problems in mathematics.  Calculus cannot be learned by observation.  The student must become an active participant by reading the text, paying attention in class, and, most importantly, by working the homework exercises.  The more exercises one works the better.  As a general rule, the student should spend a minimum of two hours outside of class for every one hour spent in class.

 

LEARNING OBJECTIVES AND ACTIVITIES

 

 

MODULE ONE – ACCUMULATING CHANGE PART ONE

 

Section 6.1    Results of Change and Area Approximations

 

Objectives:     Students should be able to:

 

  • interpret the area of a region between a rate-of-change graph and the horizontal axis as the accumulation of change,
  • approximate the area of a region between a function and the horizontal axis using left rectangles, right rectangles, or midpoint rectangles,
  • appropriately label and interpret the area of a region, and
  • discern between rate-of-change data and count data.

 

Assignment:   Read and study pages 368–378 in your text.

 

Work:              Pages 378–386:  1,5,7,15,19,27.

 

 

Section 6.2    Limits of Sums, Accumulated Change, and the Definite Integral

 

Objectives:     Students should be able to:

 

  • numerically approximate the area of a region between a non-negative function and the horizontal axis as the limiting value of sums of areas of midpoint rectangles, and
  • write the definite integral notation representing the area (or the negative of the area) of a region between a function and the x-axis if the function does not cross the x-axis between a and b.

 

Assignment:   Read and study pages 386-394 in your text.

 

Work:              Pages: 394-400:  1,3,7,9,11,17

 

 

Section 6.3    Accumulation Functions

 

Objectives:     Students should be able to:

 

  • sketch an accumulation function using estimated grid areas,
  • sketch graphs of accumulation functions with different starting points,
  • sketch a general accumulation function graph, and
  • recover a function from its rate of change equation.

 

Assignment:   Read and study pages 400-410 in your text.

 

Work:              Pages: 410-414:  1,3,5,9,11,15,19,21,23.           

To prepare for the Module One Test:

 

Ø      Attend all classes.

 

Ø      Read all assignments.

 

Ø      Do all homework and work all the problems stated in the syllabus.

 

Ø      Read the Chapter 6 Summary on page 464, topics: Approximating Results of Change, and Limits of Sums and Accumulation Functions.

 

Ø      Work the Concept Check problems, page 465, Sections 6.1, 6.2, and 6.3

 

Ø      Work the Chapter 6 Review Test, page 466:  1-3

 

MODULE TWO – ACCUMULATING CHANGE PART TWO

 

 

Section 6.4    The Fundamental Theorem

 

Objectives:     Students should be able to:

 

  • write the algebraic antiderivatives of functions of the form k, xn, bx, and .,
  • use the Sum Rule and the Constant Multiplier Rule for antiderivatives,
  • interpret the Fundamental Theorem as the connection between antiderivatives and derivatives,
  • find general and specific antiderivatives, and
  • use the Fundamental Theorem to check antiderivatives.

 

Assignment:   Read and study pages 415-426 in your text.

 

Work:              Pages 426-428: 9,11,13,15,17,19,23,25,27,33.

 

 

Section 6.5    The Definite Integral

 

Objectives:     Students should be able to:

 

  • evaluate and interpret a definite integral,
  • use definite integrals to calculate the area of a region between two curves, and
  • use the definite integral to find the difference of two accumulated changes.

 

Assignment:   Read and study pages 429-441 in your text.

 

Work:              Pages: 441-447: 1,3,5,7,9,11,13,15,19,21,25,27,29,31.

 

 

To prepare for the Module Two test:

 

Ø      Attend all classes.

 

Ø      Read all assignments.

 

Ø      Do all homework and work all the problems stated in the syllabus.

 

Ø      Read the Chapter 6 Summary on pages 464-465, topics:  The

Fundamental Theorem of Calculus, and The Definite Integral.

 

Ø      Work the Concept Check problems, page 465, Sections 6.4 and 6.5.

 

Ø      Work the Chapter 6 Review Test, page 466: 4, & 5.

 

 

MODULE THREE – ANALYZING ACCUMULATED CHANGE

 

 

Section 7.1    Perpetual Accumulation and Improper Integrals

 

Objectives:     Students should be able to:

 

  • evaluate improper integrals, and
  • recognize that an improper integral diverges.

 

Assignment:   Read and study pages 472-475 in your text.

 

Work:              Pages 475-476:  1,3,5,7,9,13,15.

 

 

Section 7.2    Streams in Business and Biology

 

Objectives:     Student should be able to:

 

  • use definite integrals to estimate future and present values of a continuous stream, and
  • use definite integrals to estimate the future value of a biological stream.

 

Assignment:   Read and study pages 476-486 in your text. Omit “discrete income streams”, pp. 482-485.

 

Work:              Pages 486-490:  1a,3,5,7a,13a,15,17a & b,19,21.

 

 

Section 7.3    Integrals in Economics

 

Objectives:     Student should be able to use definite and improper integrals and demand and supply curves to find and interpret:

 

  • consumers’ willingness and ability to spend,
  • consumers’ expenditure,
  • consumers’ surplus,
  • producer’s willingness and ability to supply (receive),
  • total revenue,
  • producer’s surplus,
  • market equilibrium, and
  • total social gain.

 

Assignment:   Read and study pages 492-506 in your text.

 

Work:              Pages 506-511: 1,2,3,5,7,8,9,11,13, 15,17.

 

 

 

To prepare for the Module Three test:

 

Ø      Attend all classes.

 

Ø      Read all assignments.

 

Ø      Do all homework and work all the problems stated in the syllabus.

 

Ø      Read the Chapter 7 Summary on pages 535-536, topics:  Improper Integrals, Streams in Business and Biology, and Integrals in Economics.

 

Ø      Work the Concept Check problems, page 537, Sections 7.1, 7.2, and 7.3.

 

Ø      Work the Chapter 7 Review Test, pages 537-538:  1,3,4.

 

MODULE FOUR – MULTIVARIABLE CHANGE:  MODELS, GRAPHS, RATES

 

 

Section 9.1    Multivariable Functions and Contour Graphs

 

Objectives:     Students should be able to:

 

  • read inputs and outputs from a table of multivariable data,
  • calculate outputs and inputs using multivariable functions,
  • sketch contours on table of data
  • sketch contours given an equation,
  • solve multivariable functions for contour formulas,
  • estimate output and change in output using contour graphs, and
  • determine the direction of steepest descent from contour graphs

 

Assignment:   Read and study pages 598-609 in your text.

 

Work:              Pages 610-620: 1,3,5,7,9,11,13,17,21,25,29

 

 

Section 9.2    Cross-Sectional Models and Rates of Change

 

Objectives:     Students should be able to:

 

  • fit models to cross-sections of data and interpret them,
  • interpret cross-sections of multivariable functions,
  • find the rate of change of a cross-section from a table, and
  • find the rate of change of a cross-section from a multivariable function.

 

Assignment:   Read and study pages 621-627 in your text.

 

Work:              Pages 628-634: 1,3,5a,5b,9,13,15,21.

 

 

Section 9.3    Partial Rates of Change

 

Objectives:     Students should be able to:

 

  • write partial derivative formulas,
  • interpret partial derivatives as partial rates of change,
  • write second partial derivatives of multivariable functions, and
  • write a second partials matrix.

 

Assignment:   Read and study pages 635-640 and 641-642 (omit “Concept Development:  Interpreting Second Partials” on pages 640-641) in your text.

 

Work:              Pages 643-648: 1,3,5,7,9,10,11,12,13,15,19,23,24d,29.

 

 

Section 9.4    Compensating for Change

 

Objectives:     Students should be able to:

 

  • calculate the change needed in one variable to compensate for a change in another variable,
  • interpret compensation for change graphically as motion along a contour curve, and
  • use derivatives and slopes of tangent lines to estimate the needed compensation.

 

Assignment:   Read and study pages 648-656 in your text.

 

Work:              pages 656-659: 1,3,5,7,9,21

 

 

To prepare for the Module Four test:

 

Ø      Attend all classes.

 

Ø      Read all assignments.

 

Ø      Do all homework and work all the problems stated in the syllabus.

 

Ø      Read the Chapter 9 Summary on page 660.

 

Ø      Work the Concept Check problems on page 661.

 

Ø      Work the Chapter 9 Review test, pages 662-663:  1-4

 

 

 

 

 

 

 

 

 

                                                                                                                     


MODULE FIVE – ANALYZING MULTIVARIABLE CHANGE: OPTIMIZATION

 

 

Section 10.1  Multivariable Critical Points

 

Objectives:     Students should be able to:

 

  • identify relative and absolute extrema on tables and contour graphs,
  • identify saddle points on tables and contour graphs, and
  • identify critical points on graphs of three-dimensional functions.

 

Assignment:   Read and study pages 668-676 in your text.

 

Work:              pages 676-686:  1,2,3,5,7,9,13,19,21

 

 

Section 10.2  Multivariable Optimization

 

Objectives:     Students should be able to:

 

  • identify critical points on multivariable functions as points where all partial derivatives equal 0,
  • interpret critical points on multivariable functions as points where the lines tangent to the surface are horizontal,
  • solve systems of partial derivative equations to locate critical points,
  • use the determinant test to identify the type of critical point found, and
  • use contour graphs to identify the type of critical point found.

 

Assignment:   Read and study pages 686-695 in your text.

 

Work:              Pages 695-698:  1,4,7,9,15,19

 

 

Section 10.3  Optimization Under Constraints

 

Objectives:     Students should be able to:

 

  • identify constrained optimal points as points where the constraint curve is tangent to a contour curve,
  • solve systems of partial derivative equations to locate constrained optima,
  • calculate and interpret the Lagrange multiplier,
  • use contour graphs to identify the type of extreme point found, and
  • numerically identify the type of extreme point found.

 

Assignment:   Read and study pages 699-705 in your text.

 

Work:              pages 706-709:  1,3,5b,9,11b,c,&d,15a&b

 

 

To prepare for the Module Five test:

 

Ø      Attend all classes.

 

Ø      Read all assignments.

 

Ø      Do all homework and work all the problems stated in the syllabus.

 

Ø      Read the Chapter 10 Summary on page 715, topics:  Multivariable Optimization and Optimization Under Constraints.

 

Ø      Work the Concept Check problems, page 716, Sections 10.1,10.2, and 10.3.

 

Ø      Work the Chapter 10 Review Test, pages 716-717:  1-4